Use the accompanying paired data consisting of weights of large cars (pounds) and highway fuel consumption (mi/gal). Let x represent the weight of a car and let y represent the highway fuel consumption. Use the given weight and the given confidence level to construct a prediction interval estimate of highway fuel consumption. Use x = 4400 pounds with a 99% confidence level. Click the icon to view the car weight and highway fuel consumption data. Find the indicated prediction interval. mi/gal < y < mi/gal (Round to three decimal places as needed.) Car Weight and Highway Fuel Consumption Highway Fuel Weight (pounds) Consumption (mi/gal) 3604 32 3954 28 4250 25 4001 30 3761 28 3850 29 3873 30 4664 23 4326 27 4352 27 3892 33 3951 31
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First, we need to find the equation of the regression line for the given data. We can use a calculator or software to do this, or we can use the formulas: - Slope: b = r * (Sy/Sx) - Intercept: a = ybar - b * xbar where r is the correlation coefficient, Sy is the Show more…
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Consider the following fuel consumption data X 3.4 3.8 4.1 2.2 2.6 2.9 2.0 2.7 1.9 3.4 Y 5.5 5.9 6.5 3.3 3.6 4.6 2.9 3.6 3.1 4.9 where X = weight (in 1000 pounds) and Y = fuel consumption (in mile-per-gallon). The model yi = ̠₀ + ̠₁xi + ̤i is considered. Note that SSR = 13.915 & SSyy = 14.589; ȳ = 4.39, x̄ = 2.9, and ∑(xi - x̄)" = 5.18. a. Find the least squares estimates of ̠₀ and ̠₁. b. Write down the hypotheses to test the statement that "fuel consumption of a car is affected by its weight". Give the ANOVA table and test the significance of the above statement at ̡ = 0.05. c. Suppose that a new car model is developed and the weight is designed to be 3500 pounds. Construct a 95% confidence interval for the mean mile-per-gallon for this new car model. d. If a new car is designed and its weight is 5000 pounds, can the above fitted model be used to study the corresponding fuel consumption? Comment.
Sri K.
Suppose a car is chosen at random: Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). The following information is based on data taken from Consumer Reports (Vol. 62, No.4): 27, 44, 32, 23, 40, 34, 52, y, 30, 19, 24, 13, 29, 17, 21, 14. (a) Construct a scatterplot of the miles per gallon (y) versus the weight of the car (x). (b) Compute the correlation coefficient between the weight of the car and the miles per gallon. Given that r = 0.375, Sx = 10.0845, σ = 20.875, and Sy = 6.4017 (if you want to use the formula provided in our textbook). (c) Compute the least-squares regression line for predicting the miles per gallon from the weight of the car. (d) Suppose the car weighs 38 hundreds of pounds, predict the value for y, which is the miles per gallon.
Jerelyn N.
3) Listed below are the weights (in pounds) and the highway fuel consumption amounts (in mi/gal) of randomly selected cars. Is there a linear correlation between weight and highway fuel consumption? What does the result suggest about a national program to reduce the consumption of imported oil? Fuel Consumption 27 29 27 24 37 34 37 Weight 3175 3450 3225 3985 2440 2500 2290 a) What is the explanatory variable? What is the response variable? (5 points) b) Draw a scatter plot of the data. Remember to include name, label horizontal and vertical axis. (8points) c) Is there sufficient evidence to conclude that there is a relationship between car weight and fuel consumption? Solve using the traditional method, p- value analysis, and clearly explain the meaning of the correlation in your decision rule. Use α = 0.05 (20 points) d)Find the best predicted fuel consumption for a car that weighs 3450 pounds and clearly explain what your answer is telling you in a couple of sentences (10 points). What is the Residual value (8 points)? Is the regression over estimating, underestimating the actual or is it pretty close. Explain. e) Construct a 95% confidence interval for the true slope β₁ and interpret. (17 points)
David N.
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